Question

The given table shows the months of birth of 40 students of class IX of a particular section in a

school.
If one student is chosen at random, find the probability that the student is born:

a) in the later half of the year.

b) in the month having 31 days.

c) in the month having 30 days.​

Answer 1

Answer:

Total number of students in the class = 40. (i) Let E 1 E1 be the event that the chosen student is born in the latter half of the year . Then , P ( E 1 ) = no., of students born in latter half of the year total number of students P(E1)=no., of students born in latter half of the year total number of students = 2 + 6 + 3 + 4 + 4 + 4 40 = 23 40 = 0.575 =2+6+3+4+4+440=2340=0.575 (ii) Let E 2 E2 be the event that the chosen student is born in a month having 31 days . then , P ( E 2 ) = number of students born in a month having 31 days total number of students P(E2)=number of students born in a month having 31 daystotal number of students = 3 + 2 + 5 + 2 + 6 + 4 + 4 40 = 26 40 = 13 20 = 0.65 =3+2+5+2+6+4+440=2640=1320=0.65 (iii) Let E 3 E3 be the event that the chosen student is born in a month having 30 days . then , P ( E 2 ) = number of students born in a month having 30 days total number of students P(E2)=number of students born in a month having 30 daystotal number of students = 2 + 1 + 3 + 4 40 = 10 40 = 1 4 = 0.25 2+1+3+440=1040=14=0.25.

Answer 2

Answer:

Total number of students in the class $=40$.

Step-by-step explanation:

Step 1: Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. A probability is a number between 0 and 1, where 1 indicates certainty and 0 indicates impossibility of the event.

(i) Let $E_1$ be the event that the chosen student is born in the latter half of the year. Then ,

$\begin{aligned}& P\left(E_1\right)=\frac{\text { no., of students born in latter half of the year }}{\text { total number of students }} \\& =\frac{2+6+3+4+4+4}{40}=\frac{23}{40}=0.575\end{aligned}$

Step 2:(ii) Let $E_2$ be the event that the chosen student is born in a month having 31 days . then ,

$\begin{aligned}& P\left(E_2\right)=\frac{\text { number of students born in a month having } 31 \text { days }}{\text { total number of students }} \\& =\frac{3+2+5+2+6+4+4}{40}=\frac{26}{40}=\frac{13}{20}=0.65\end{aligned}$

Step 3:(iii) Let $E_3$ be the event that the chosen student is born in a month having 30 days . then ,

$\begin{aligned}& P\left(E_2\right)=\frac{\text { number of students born in a month having } 30 \text { days }}{\text { total number of students }} \\& =\frac{2+1+3+4}{40}=\frac{10}{40}=\frac{1}{4}=0.25 .\end{aligned}$

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